1. when you think that your child's future, intellectual growth and education are affected
2. when you think that you have better things to do with your time than advocacy (as in a job situation that will not allow you to spend time on gifted advocacy)
3. you live in an area where there are excellent private schools as well as excellent after schooling opportunities
4. when you are sure that the best the school district could potentially offer will not come close to what your child needs in terms of acceleration or instruction.
5. when you feel that your child is wasting his time every day by being physically present in a classroom because he is made to do it and he knows more than what he is "supposed" to know at that grade level.
I reached all these points and decided to move on to private schools.

The first thing that I noticed is how much "more" the teachers are able and willing to do for a lower pay scale at the private school (e.g. yard duty, curbside drop off supervision, decorating classroom for festivals, running math bees and spelling bees, making their own photocopies, teaching without aides) - I am mentioning this because I spent a year of my personal time volunteering for these things at my PS where the teachers were whining about budget cuts and hence needing parental help for these things!

I got better response for my questions from private school, they accounted for every minute of the day that my son spent there (no wasting time at all), my son got "extras" that he could not have gotten in addition to the acceleration in curriculum (computer programming, music specialist, foreign language, sports specialist, character education, science labs etc). I am happy to not be dealing with PS anymore and spend more of time on my career related issues these days.

As Frog says, investigate your private school options - shadow their classrooms if you can. In our case, we made 3 moves before things clicked - but all the moves were progressively better for my DS.
Good luck.